private List<Operator> alg(List<Fact> state, List<List<Fact>> history,
			List<Operator> path) {
		List<Operator> result = null;

		// final state included in current state => WIN
		if (state.containsAll(finalState)) {
			result = new ArrayList<Operator>();
			result.addAll(path);
		} else {
			List<Operator> viableActions = viableActions(state, history);
			if (viableActions.isEmpty()) { // no possible actions => FAIL
				result = null;
			} else {
				// choose operator
				Operator chosen = viableActions.get(0);
				List<Fact> newState = applyOperator(state, chosen);

				history.add(state);

				// recursive call
				path.add(chosen);
				List<Operator> call = alg(newState, history, path);
				path.remove(path.size() - 1);

				if (call == null) {
					viableActions.remove(chosen);
					if (viableActions.isEmpty()) {
						result = null;
					} else {
						// choose next operator from the list
						chosen = viableActions.get(0);
						newState = applyOperator(state, chosen);

						// recursive call
						path.add(chosen);
						result = alg(newState, history, path);
						path.remove(path.size() - 1);
					}
				} else {
					result = call;
				}

				history.remove(state);
			}
		}
		return result;
	}